Constraints on the reciprocal propagation of a quantum particle through a one-dimensional localized complex potential

2013 ◽  
Vol 91 (3) ◽  
pp. 246-250
Author(s):  
Ethan Knox ◽  
P.T. Leung
Keyword(s):  
Complex Potential ◽  
Quantum Particle ◽  
Incident Beam ◽  
Real Potential ◽  
Reflected Waves ◽  
One Dimensional ◽  
Numerical Studies ◽  
Reciprocity Relations ◽  
Left And Right ◽  
Complete Analogy

In the propagation of an electron through a one-dimensional asymmetric complex potential, it is known that while the conventional Green function reciprocity symmetry will ensure transmission to be symmetric between a “left-incident” and a “right-incident” beam, no such symmetry exists for the case of reflection. Here we derive generalized reciprocity relations for both the amplitude and phase of the reflected waves as constraints on the left- and right-incident beams, in complete analogy to what was established in optics. We further provide illustrations of these relations via direct analytical calculations in the case of a real potential, and via numerical studies in the case of a complex potential.

scholarly journals Numerical Modeling of the Interaction of Solitary Waves and Submerged Breakwaters with Sharp Vertical Edges Using One-Dimensional Beji & Nadaoka Extended Boussinesq Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Mohammad H. Jabbari ◽  
Parviz Ghadimi ◽  
Ali Masoudi ◽  
Mohammad R. Baradaran
Keyword(s):  
Solitary Waves ◽  
Numerical Study ◽  
Time Integration ◽  
Boussinesq Equations ◽  
Linear Interpolation ◽  
Reflected Waves ◽  
One Dimensional ◽  
Propagating Waves ◽  
Linear Elements ◽  
Predictor Corrector

Using one-dimensional Beji & Nadaoka extended Boussinesq equation, a numerical study of solitary waves over submerged breakwaters has been conducted. Two different obstacles of rectangular as well as circular geometries over the seabed inside a channel have been considered in view of solitary waves passing by. Since these bars possess sharp vertical edges, they cannot directly be modeled by Boussinesq equations. Thus, sharply sloped lines over a short span have replaced the vertical sides, and the interactions of waves including reflection, transmission, and dispersion over the seabed with circular and rectangular shapes during the propagation have been investigated. In this numerical simulation, finite element scheme has been used for spatial discretization. Linear elements along with linear interpolation functions have been utilized for velocity components and the water surface elevation. For time integration, a fourth-order Adams-Bashforth-Moulton predictor-corrector method has been applied. Results indicate that neglecting the vertical edges and ignoring the vortex shedding would have minimal effect on the propagating waves and reflected waves with weak nonlinearity.

Comparison of iterative desmearing procedures for one-dimensional small-angle scattering data

2011 ◽  
Vol 44 (1) ◽  
pp. 32-42 ◽  
Author(s):  
Thomas Vad ◽  
Wiebke F. C. Sager
Keyword(s):  
Small Angle ◽  
Incident Beam ◽  
Scattering Data ◽  
Data Sets ◽  
Convergence Criteria ◽  
Small Momentum Transfer ◽  
One Dimensional ◽  
Noise Filter ◽  
Large Numbers ◽  
Angle Scattering

Two simple iterative desmearing procedures – the Lake algorithm and the Van Cittert method – have been investigated by introducing different convergence criteria using both synthetic and experimental small-angle neutron scattering data. Implementing appropriate convergence criteria resulted in stable and reliable solutions in correcting resolution errors originating from instrumental smearing,i.e.finite collimation and polychromaticity of the incident beam. Deviations at small momentum transfer for concentrated ensembles of spheres encountered in earlier studies are not observed. Amplification of statistical errors can be reduced by applying a noise filter after desmearing. In most cases investigated, the modified Lake algorithm yields better results with a significantly smaller number of iterations and is, therefore, suitable for automated desmearing of large numbers of data sets.

scholarly journals Contact Electrification by Quantum-Mechanical Tunneling

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Morten Willatzen ◽  
Zhong Lin Wang
Keyword(s):  
Potential Versus ◽  
Coulomb Repulsion ◽  
Quantum Mechanical ◽  
Quantum Mechanical Tunneling ◽  
One Dimensional ◽  
Contact Electrification ◽  
Order Of Magnitude ◽  
Left And Right ◽  
Tunneling Dynamics ◽  
Vacuum Gap

A simple model of charge transfer by loss-less quantum-mechanical tunneling between two solids is proposed. The model is applicable to electron transport and contact electrification between e.g. a metal and a dielectric solid. Based on a one-dimensional effective-mass Hamiltonian, the tunneling transmission coefficient of electrons through a barrier from one solid to another solid is calculated analytically. The transport rate (current) of electrons is found using the Tsu-Esaki equation and accounting for different Fermi functions of the two solids. We show that the tunneling dynamics is very sensitive to the vacuum potential versus the two solids conduction-band edges and the thickness of the vacuum gap. The relevant time constants for tunneling and contact electrification, relevant for triboelectricity, can vary over several orders of magnitude when the vacuum gap changes by one order of magnitude, say, 1 Å to 10 Å. Coulomb repulsion between electrons on the left and right material surfaces is accounted for in the tunneling dynamics.

SMALL-TO-LARGE POLARON CROSSOVER IN ONE DIMENSION USING VARIATIONAL PHONON-AVERAGING TECHNIQUES

2001 ◽  
Vol 15 (13) ◽  
pp. 1923-1937 ◽  
Author(s):  
P. CHOUDHURY ◽  
A. N. DAS
Keyword(s):  
One Dimension ◽  
Density Matrix Renormalization Group ◽  
Phonon Coupling ◽  
One Dimensional ◽  
Variational Techniques ◽  
Density Matrix Renormalization ◽  
Numerical Studies ◽  
Real Picture ◽  
Analytical Approaches ◽  
Averaging Techniques

The ground-state properties of polarons in a one-dimensional chain is studied analytically within the modified Lang–Firsov (MLF) transformation using various phonon-averaging techniques. The object of the work is to examine how the analytical approaches may be improved to give rise to the real picture of polaronic properties as predicted by extensive numerical studies. The results are compared with those obtained from numerical analyses using the density matrix renormalization group (DMRG) and other variational techniques. It is observed that our results agree well with the numerical results particularly in the low and intermediate range of phonon coupling.

scholarly journals Determination of hard X-ray polarization from two-dimensional images

2020 ◽  
Vol 53 (6) ◽  
pp. 1559-1561
Author(s):  
Robert B. Von Dreele ◽  
Wenqian Xu
Keyword(s):  
Incident Beam ◽  
Beam Polarization ◽  
Two Dimensional ◽  
One Dimensional ◽  
X Ray ◽  
Dimensional Image ◽  
Two Dimensional Image ◽  
The Difference ◽  
Two Dimensional Images

An estimate of synchrotron hard X-ray incident beam polarization is obtained by partial two-dimensional image masking followed by integration. With the correct polarization applied to each pixel in the image, the resulting one-dimensional pattern shows no discontinuities arising from the application of the mask. Minimization of the difference between the sums of the masked and unmasked powder patterns allows estimation of the polarization to ±0.001.

Experimental investigation on the secondary instability of liquid-fluidized beds and the formation of bubbles

2002 ◽  
Vol 470 ◽  
pp. 359-382 ◽  
Author(s):  
PAUL DURU ◽  
ÉLISABETH GUAZZELLI
Keyword(s):  
Fluidized Beds ◽  
Secondary Instability ◽  
Analytical Models ◽  
Physical Origin ◽  
Weakly Nonlinear ◽  
One Dimensional ◽  
Numerical Studies ◽  
Wavy Structure ◽  
Nonlinear Simulations ◽  
The One

The objective of the present work is to investigate experimentally the secondary instability of the one-dimensional voidage waves occurring in two-dimensional liquid- fluidized beds and to examine the physical origin of bubbles, i.e. regions devoid of particles, which arise in fluidization. In the case of moderate-density glass particles, we observe the formation of transient buoyant blobs clearly resulting from the destabilization of the one-dimensional wavy structure. With metallic beads of the same size but larger density, the same destabilization occurs but it leads to the formation of real bubbles. Comparison with previous analytical and numerical studies is attempted. Whereas the linear and weakly nonlinear analytical models are not appropriate, the direct nonlinear simulations provide a qualitative agreement with the observed destabilization mechanism.

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